Modern commercial and personal business transactions involving the transfer of funds or other assets from one or more accounts to one or more other accounts are being carried out more and more via electronic means. Very often, such transactions are effected across an insecure transmission medium such as the Internet using a certain degree of encryption. The ability of hackers to intercept and decrypt such messages is notoriously well known, and it is widely acknowledged that the degree of encryption currently permitted by the U.S. government is insufficient to protect sensitive information communicated over such insecure transaction communications media. Thus, it will be apparent to those skilled in the art that it would be highly desirable to provide a system which undoubtedly achieves comprehensive and unbreakable transmission of sensitive information involving transactions over insecure communications media such as the Internet.